Modified D-timed Petri nets, timeouts, and modelling of communication protocols

Abstract

Modified D-timed Petri nets are Petri nets with ”spe- cial” arcs to interrupt firing transitions, and with deter- ministic firing times; these special arcs are called ”in- terrupt” arcs. It is shown that the behaviour of simple modified bounded free-choice D-timed Petri nets can be represented by finite probabilistic state graphs, stationary probabilities of states can thus be obtained by standard techniques used for analysis of Markov chains. An imme- diate application of such a model is performance analysis of systems of interacting asynchronous processes, and in particular communication protocols. Places of Petri nets model queues of messages, transitions represent events in communication networks, interrupt arcs conveniently model timeouts, and probabilities associated with free- choice classes correspond to relative frequencies of random events. A simple protocol based on unnumbered messages and acknowledgements is used as an illustration of analy- sis.